Year: 2010
Type: preprint
Abstract: For standard eigenvalue problems, a closed-form expression for the condition numbers of a multiple eigenvalue is known. In particular, they are uniformly 1 in the Hermitian case, and generally take different values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers of a multiple eigenvalue. Our main result is that a multiple eigenvalue generally has multiple condition numbers, even in the Hermitian definite case. The condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors.
Source: arXiv (Cornell University)
Author: Nakatsukasa, Yuji
Institution: University of California, Davis
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1539414217